Chapter 23

Given four measured values for the independent variable \(x\) as \(x_{1}=2.0, x_{2}=4.0, x_{3}=5.0, x_{4}=6.0\) and four corresponding measured values for the dependent variable \(y\) as \(y_{1}=2.5, y_{2}=4.5, y_{3}=7.0, y_{4}=8.5\), use the method of least squares to determine the constants \(a\) and \(b\) that give the best linear function \(y=a x+b\) that represents this measured relationship.

Given that the \(x\) value determining one standard deviation in the normal curve \(y=\frac{1}{c \sqrt{\pi}} e^{-\left(x^{2} / c^{2}\right)}\) occurs at an inflection point of the curve, show that this value is given by \(x=\) \(c / \sqrt{2}\)

Using Figure 23.4, show how Playfair concluded that "never at any former period [i.e., before 1820\(]\) was wheatso cheap, in proportion to mechanical labour, as it is at the present time [1821]."

Describe why the publication of Nightingale's pie charts would have led to an outcry in Britain. Find out what happened in the hospitals after these were published and write, a brief report.